Average Error: 0.0 → 0.0
Time: 7.2s
Precision: 64
\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]
↓
\[\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]
\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b
↓
\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r15264 = x;
        double r15265 = y;
        double r15266 = 1.0;
        double r15267 = r15265 - r15266;
        double r15268 = z;
        double r15269 = r15267 * r15268;
        double r15270 = r15264 - r15269;
        double r15271 = t;
        double r15272 = r15271 - r15266;
        double r15273 = a;
        double r15274 = r15272 * r15273;
        double r15275 = r15270 - r15274;
        double r15276 = r15265 + r15271;
        double r15277 = 2.0;
        double r15278 = r15276 - r15277;
        double r15279 = b;
        double r15280 = r15278 * r15279;
        double r15281 = r15275 + r15280;
        return r15281;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r15282 = b;
        double r15283 = y;
        double r15284 = t;
        double r15285 = r15283 + r15284;
        double r15286 = 2.0;
        double r15287 = r15285 - r15286;
        double r15288 = 1.0;
        double r15289 = r15288 - r15283;
        double r15290 = z;
        double r15291 = a;
        double r15292 = r15288 - r15284;
        double r15293 = x;
        double r15294 = fma(r15291, r15292, r15293);
        double r15295 = fma(r15289, r15290, r15294);
        double r15296 = fma(r15282, r15287, r15295);
        return r15296;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Derivation

  1. Initial program 0.0

    \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(b, \left(y + t\right) - 2, \mathsf{fma}\left(1 - y, z, \mathsf{fma}\left(a, 1 - t, x\right)\right)\right)\]

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1) z)) (* (- t 1) a)) (* (- (+ y t) 2) b)))